In congestion games (see [1]}, [2]}) we have a set of facilities \(F\) . Each player \(i\)  has a collection of subsets \(S^i_1,...,S^i_{m_i}\subset F\)  which are her actions. Given an action profile \(S=(S^1,...,S^n)\)  the congestion on each facility \(f\)  is defined to be the number of players that use this facility (i.e., \(c_f(S)=|\lbrace i:f\in S^i\rbrace |\) ). Each facility has a cost function \(l:[n]\rightarrow \mathbb {R}\)  and the utility of player \(i\)  is defined to be
\(u_i(S^1,...,S^n)=\sum _{f\in S^i} l(c_f(S))\) ; namely, each player pays the total costs of all facilities she has chosen. In explicit congestion games the possible actions of players (i.e., \(S^i_1,...,S^i_{m_i}\subset F\) ) are given explicitly.
